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Fractionalcontributionsofmicroscopicdiffusionmechanismsforcommondopantsandself-diffusioninsilicon
Ant Ural,
a)
Peter B. Grifﬁn, and James D. Plummer
Department of Electrical Engineering, Stanford University, Stanford, California 94305
Received 2 October 1998; accepted for publication 29 January 1999
An identical set of thermal oxidation and nitridation experiments has been performed for fourcommon dopants and self-diffusion in Si. Selectively perturbing the equilibrium point-defectconcentrations by these surface reactions is a powerful tool for identifying the relative importanceof the various atomic-scale diffusion mechanisms. We obtain bounds on the fractional contributionsof the self-interstitial, vacancy, and concerted exchange mechanisms for arsenic, boron, phosphorus,antimony, and self-diffusion in Si at temperatures of 1100 and 1000°C. These bounds are found bysimultaneously solving a system of equations making only very conservative assumptions. Thevalidity of common approximations found in previous work and their effects on the results are alsoanalyzed in detail. We ﬁnd that B and P diffuse by a self-interstitial mechanism, whereas Sbdiffusion is almost exclusively vacancy mediated. As and self-diffusion, on the other hand, exhibitevidence for a dual vacancy-interstitial mechanism with the possibility of some concerted exchangecomponent. ©
1999 American Institute of Physics.
S0021-8979
99
05109-9
I.INTRODUCTION
Diffusion of substitutional dopants in Si can be mediatedon the atomic scale by either native point defects, namelyself-interstitials and vacancies, or by a direct exchangemechanism which occurs in their absence.
1–6
Theoretical cal-culations have predicted that concerted exchange, in whichtwo adjacent substitutional atoms switch positions, is such apossible direct mechanism.
7
The relative contribution of eachof these three mechanisms for a given dopant is a fundamen-tal property reﬂecting the complicated many-body energeticsoccurring on the atomic scale. It is also of signiﬁcant practi-cal importance for semiconductor devices, since most fabri-cation processes such as oxidation and ion-implantation per-turb the equilibrium point-defect concentrations. The mannerin which these perturbations affect the diffusion of a givendopant depends on what fraction of its diffusion is mediatedby the perturbed point defect. As a result, an identical pro-cess may affect the diffusivity of each dopant in a signiﬁ-cantly different manner.In this article, we take advantage of this fact to deter-mine bounds on the self-interstitial
I
, vacancy
V
, and con-certed exchange
CE
mediated fractions of diffusion for fourcommon dopants
As, B, P, and Sb
and self-diffusion in Si.We use two well-studied surface reactions, thermal oxidationand nitridation, to selectively perturb the equilibrium point-defect concentrations. Although the details of these surfacereactions are not fully understood, it has been well estab-lished that thermal oxidation injects self-interstitials, whereasnitridation results in vacancy injection into the bulk.
4
Thecomplementary nature of these two processes enables us todraw conclusions about the relative importance of each mi-croscopic diffusion mechanism for each dopant. This ideahas been utilized in the past in similar experiments.
4,8–12
Ourexperiments offer improvement in a variety of ways. First of all, we perform an extensive set of
identical
oxidation andnitridation experiments at two temperatures for four dopantsand self-diffusion, and solve the resulting system of equa-tions simultaneously. We carry out this solution numericallyrather than using analytic arguments as commonly donepreviously.
4,9–12
In addition, we use secondary ion massspectrometry
SIMS
to obtain the diffusion proﬁles,whereas some of the earlier work used spreading resistanceanalysis, which has a much poorer depth resolution.
4,9,10
Fur-thermore, we do not initially make any assumptions aboutthe point-defect injection levels or mechanisms that resultfrom oxidation and nitridation, nor about the fractional con-tributions of various diffusion mechanisms for any of thedopants. One of the most signiﬁcant improvements is that weinclude the possibility of a CE mechanism in our analysis of As and self-diffusion, which previous studies have almostalways ignored without convincing arguments. After solvingfor this general case, we also analyze the consequences of making some of the assumptions commonly found in theliterature. The conclusions we arrive at for B, P, and Sbagree well with previous results.
4,9–12
The self-diffusion re-sults, which have been recently published,
13
show clear evi-dence of a dual vacancy-interstitial mechanism. The mostimportant outcome of this work is that the inconsistency ob-served previously in the oxidation and nitridation data forAs
4,9,14
is resolved. We ﬁnd that As diffusion can be ana-lyzed within the same framework as the other dopants, andthat it diffuses via a dual vacancy-interstitial mechanism,with the possibility of a CE component.In what follows, unless otherwise stated, the word‘‘equilibrium’’ refers to a condition where thermal equilib-rium concentrations of point defects prevail, and ‘‘nonequi-librium’’ indicates that these concentrations have been per-turbed by an external excitation.
a
Electronic mail: antural@leland.stanford.eduJOURNAL OF APPLIED PHYSICS VOLUME 85, NUMBER 9 1 MAY 1999
64400021-8979/99/85(9)/6440/7/$15.00 © 1999 American Institute of Physics
Downloaded 06 Nov 2002 to 171.64.101.210. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp
II.EXPERIMENTALPROCEDURE
Five structures were fabricated for this experiment, onefor each dopant. For the As, P, and Sb structures, a 15 nmscreen oxide was grown thermally on 5–10
,
n
-type
100
CZ silicon wafers, followed by ion implantation of As, P,and Sb at 110 keV to a dose of 1
10
14
cm
2
, at 70 keV toa dose of 2
10
14
cm
2
, and at 140 keV to a dose of 1
10
14
cm
2
, respectively. The tilt angle was 7° with no ro-tation of the wafers. Following implantation, a drive-in inertanneal at 1100°C was performed for 5 h, and an intrinsicsilicon surface layer was grown epitaxially by chemical va-por deposition
CVD
. For As and Sb, this surface layer wasroughly 400 nm, whereas for faster diffusing P, 800 nm. TheB structure was fabricated by CVD growth of a 1000 nmintrinsic Si layer, followed by a roughly 350 nm boron dopedsurface layer. In all structures, the peak concentrations of thedopants were kept at around a few 10
18
cm
3
, avoiding com-plications that could arise from extrinsic doping effects. Fi-nally, the Si isotope structure was grown by CVD with asurface layer of roughly 300 nm containing the three stableisotopes of silicon in their natural relative abundances, and aburied layer heavily depleted in
29
Si and
30
Si. For example,
30
Si, the isotope used to monitor self-diffusion, was reducedfrom a natural abundance of 3.10% at the surface to 0.002%at the buried layer. This transition was graded due to Siautodoping effects during predeposition cleaning.These ﬁve structures, one for each dopant, were thenannealed in a furnace in inert
100% Ar
, nitridizing
100%NH
3
, and oxidizing
100% O
2
ambients at 1100 and1000°C for 1 and 5 h, respectively. The average oxide thick-ness grown was 126.5 and 163.4 nm for the 1100 and1000°C dry oxidations, respectively. Measurement of nitridethicknesses revealed an average value of 3.6 and 3.1 nm,respectively, for the 1100 and 1000°C experiments.The six resulting diffusion proﬁles, along with the as-grown proﬁle for each dopant were obtained by SIMS. SIMSanalysis for As, P, and Sb were performed on aCAMECA-3
f
instrument with a 14.5 keV Cs
primarybeam at a sputtering rate of 40, 20, and 8 Å/s, respectively.The B and
30
Si proﬁles were analyzed on a CAMECA-4
f
instrument with an 8 keV O
2
primary beam at a sputteringrate of 35 and 5 Å/s, respectively. A high mass resolutiongreater than 3500 was used for
30
Si to distinguish it from
29
Si–H.The diffusion coefﬁcient for each case was extracted bytaking the as-grown proﬁle, and using TSUPREM-4,
15
a pro-cess simulator, to numerically diffuse it until a match wasachieved with the SIMS proﬁle after annealing. The best ﬁtwas determined by minimizing the root-mean-square error.Furnace ramp up and down effects were properly taken intoaccount. The solution of Fick’s law provided a single diffu-sion coefﬁcient for each case.Diffusivity enhancements or retardations were computedfor each oxidation or nitridation experiment by normalizingthe extracted nonequilibrium diffusion coefﬁcient by the cor-responding value obtained from the inert anneal. Using theseenhancement and retardation values, bounds for the frac-tional contributions of the three diffusion mechanisms foreach dopant were found using AMPL,
16
a mathematical pro-gramming tool.
III.THEORY
Before we proceed to the results of the experiments, weneed to derive the equations used to ﬁnd the fractional con-tributions of the various mechanisms from diffusivity en-hancement or retardation data. First, we need to note that thediffusivity coefﬁcient,
D
A
, for a dopant
A
under both equi-librium and nonequilibrium conditions is given by
D
A
X
d
AX
C
AX
C
A
,
1
where
A
, in our case, is As, B, P, Sb, or Si, and
X
is themechanism of diffusion
X
I, V, or CE
.
C
AX
and
d
AX
arethe concentration and diffusivity, respectively, of the defect
AX
whose migration determines the
X
mechanism mediateddiffusion of species
A
. For example, this migrating defectcould be a dopant-defect pair, an interstitial dopant, or asingle native point defect.
C
A
is the total concentration of thesubstitutional dopant
A
. For P diffusion, for instance, theo-retical calculations have predicted that the phosphorous-interstitial (P
i
) and phosphorous-vacancy pair
PV
are therelevant defects which determine P diffusion by an I and Vmediated mechanism, respectively.
3
For the CE mechanism,the corresponding defect is the substitutional phosphorus(P
s
) itself. To simplify the analysis, it is customary to deﬁnethe
X
mechanism mediated fraction of
A
diffusion
under equilibrium
as
f
AX
d
AX
C
AX
eq
/
C
A
D
A
eq
.
2
Here, the superscript eq denotes equilibrium conditions.Combining Eqs.
1
and
2
, we can write the diffusivityratio that occurs under nonequilibrium conditions as
D
A
D
A
eq
f
AI
C
AI
C
AI
eq
f
AV
C
AV
C
AV
eq
f
ACE
.
3
The only approximation made in Eq.
3
is that there is onlyone migrating defect
AX
which contributes to the
X
mediateddiffusion of
A
. We will come back to this point at the end of the discussion. The ratio of the diffusion coefﬁcient underoxidation to that under inert annealing gives one equation of the form Eq.
3
for each dopant. A similar equation can bewritten down for nitridation. As a result, ﬁve dopants an-nealed under identical conditions lead to ten equations with30 unknowns, since for each dopant there are six unknowns:
f
AI
,
f
ACE
,
C
AI
ox
/
C
AI
eq
,
C
AI
nit
/
C
AI
eq
,
C
AV
ox
/
C
AV
eq
, and
C
AV
nit
/
C
AV
eq
.The last four unknowns listed are the migrating defect per-turbation levels where the superscripts ox, nit, and eq denoteoxidation, nitridation, and equilibrium
inert anneal
condi-tions, respectively. The normalization condition
f
AI
f
AV
f
ACE
1 eliminates
f
AV
for each dopant. With that manyunknowns, it is virtually impossible to arrive at any non-trivial bounds on the fractional contributions of different dif-fusion mechanisms. The problem is greatly simpliﬁed if arelation is found between the concentration of the migratingdefect,
C
AX
, and that of the corresponding native
6441J. Appl. Phys., Vol. 85, No. 9, 1 May 1999 Ural, Grifﬁn, and Plummer
Downloaded 06 Nov 2002 to 171.64.101.210. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp
point defect
C
X
. The
complete
set of equations governingthe interactions between these two species are
I
A
s
⇔
AI
,
4
V
AI
⇔
A
s
,
5
V
A
s
⇔
AV
,
6
I
AV
⇔
A
s
,
7
I
V
⇔
Si,
8
where
A
s
is the substitutional dopant
A
, and Si in Eq.
8
represents bulk Si. Using this set of equations, expressionsfor the time rate of change of defect concentrations can beobtained. Assuming the concentrations have no spatial de-pendence, the expression for the migrating defect
AI
is
C
AI
t
k
4
f
C
I
C
A
s
k
4
r
C
AI
k
5
f
C
V
C
AI
k
5
r
C
A
s
,
9
where
k
’s denote the reaction rate constants with the ﬁrstindex in the subscript referring to the number of the reactionequation given above. The second index, on the other hand,indicates whether the rate constant is that of the forward
f
or reverse
r
reaction. An expression for the nonequilibriumperturbation level
C
AI
/
C
AI
eq
under steady-state conditions canbe found by setting the right side of Eq.
9
to zero anddividing by the corresponding equation found under equilib-rium:
C
AI
C
AI
eq
k
4
f
C
I
C
A
s
k
5
r
C
A
s
k
4
r
k
5
f
C
V
eq
k
4
f
C
I
eq
C
A
s
k
5
r
C
A
s
k
4
r
k
5
f
C
V
.
10
This general form can be simpliﬁed under certain specialcases. If the reactions represented by Eqs.
4
and
5
are
individually
at local chemical equilibrium both under equi-librium and nonequilibrium concentrations of point defects,Eq.
10
reduces to
C
AI
/
C
AI
eq
C
I
/
C
I
eq
.
11
This follows from taking the ratio of the two relations ob-tained from the chemical equilibrium requirement on the re-action in Eq.
4
:
C
AI
C
I
C
A
s
k
4
f
k
4
r
and
C
AI
eq
C
I
eq
C
A
s
k
4
f
k
4
r
.
12
By obtaining an analogous ratio from reaction Eq.
5
, it alsofollows that in this case,
C
I
C
V
C
I
eq
C
V
eq
.
13
Another special case is if the reaction in Eq.
5
is insig-niﬁcant compared to Eq.
4
, in which case Eq.
10
simpli-ﬁes again to Eq.
11
. If, on the other hand, Eq.
4
is insig-niﬁcant and Eq.
5
is dominant, the correct simpliﬁcationbecomes
C
AI
/
C
AI
eq
C
V
eq
/
C
V
. In general,
C
AI
/
C
AI
eq
lies some-where between these two values.A similar analysis can be performed for the migratingdefect
AV
. If the reactions in Eqs.
6
and
7
are individu-ally at local chemical equilibrium,
C
AV
/
C
AV
eq
C
V
/
C
V
eq
.
14
In the second special case, if Eq.
6
is the only dominantreaction, Eq.
14
is again the correct simpliﬁcation. If, onthe other hand, Eq.
6
is insigniﬁcant compared to Eq.
7
,
C
AV
/
C
AV
eq
C
I
eq
/
C
I
.Theoretical calculations suggest that reactions repre-sented by Eqs.
4
and
6
are energetically much more fa-vorable compared to Eqs.
5
and
7
, respectively.
3
Further-more, it has been pointed out recently that interactionsbetween migrating and native point defects such as thosegiven in Eqs.
4
–
7
individually reach local chemical equi-librium on a time scale much smaller than that typical indiffusion experiments.
17
Based on these considerations, areasonable approximation to Eq.
3
can be obtained by sub-stituting Eqs.
11
and
14
,
D
A
D
A
eq
f
AI
C
I
C
I
eq
f
AV
C
V
C
V
eq
f
ACE
.
15
This equation is the form that has been widely used in theliterature,
4,8–12
often without the exchange term,
f
ACE
.As mentioned before, Eq.
3
will have additional termsif more than one defect species contributes to the
X
mediateddiffusion of
A
. However, Eq.
15
will still be valid, if eachof these defect species is at local chemical equilibrium withthe corresponding native point defect.
IV.RESULTSANDDISCUSSION
Figure 1 shows the measured SIMS proﬁles and simula-tion ﬁts of the 1000°C, 5 h anneals for As, B, P, Sb, and
30
Siunder inert, nitridizing, and oxidizing ambients. Correspond-ing plots for the 1100°C anneals exhibit the same generaltrends. The simulation results ﬁt the experimental data wellin all cases. The extracted equilibrium
inert ambient
diffu-sion coefﬁcients, listed in Table I, agree well with previouswork for all dopants.
18
It is evident from Figs. 1
b
and 1
c
that B and P diffusion are retarded during nitridation andenhanced during oxidation. The opposite is true for Sb.These results qualitatively show that B and P diffuse mainlyby a self-interstitial mechanism, whereas Sb diffusion is va-cancy mediated. On the other hand, Figs. 1
a
and 1
e
clearly show that As and self-diffusion are enhanced by bothvacancy and interstitial injection. This gives the ﬁrst hint thatthese dopants have non-negligible vacancy and self-interstitial components of diffusion. Indeed, if either one of the point-defect mechanisms were solely dominant, a retar-dation in diffusivity would have been observed when theopposite type of defect is injected. On the other hand, if theexchange mechanism were dominant, perturbing the point-defect concentrations would not have any effect on the dif-fusivity.More quantitative information about the fractional con-tribution of each of the three mechanisms can be obtained byrepresenting the results as an underdetermined system of tenequations of the form Eq.
15
with 14 unknowns. This is amajor reduction in the number of unknowns compared to thatresulting from Eq.
3
. Still further reduction is possiblesince theoretical calculations have predicted that the activa-tion energy of CE is much larger than that of the point defect
6442 J. Appl. Phys., Vol. 85, No. 9, 1 May 1999 Ural, Grifﬁn, and Plummer
Downloaded 06 Nov 2002 to 171.64.101.210. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp
mechanisms for B, P, and Sb,
3
making its contribution neg-ligible for these dopants. Therefore, excluding the CE frac-tion in Eq.
15
for these dopants, we arrive at a system of ten equations with 11 unknowns. These unknowns are
f
BI
,
f
PI
,
f
SbI
,
f
AsI
,
f
AsCE
,
f
SiI
,
f
SiCE
,
C
I
ox
/
C
I
eq
,
C
V
ox
/
C
V
eq
,
C
I
nit
/
C
I
eq
, and
C
V
nit
/
C
V
eq
. The last four unknowns listed are thepoint defect perturbation levels where the superscripts havethe same meaning as before. Five out of the ten equations,one for each dopant, are obtained from the oxidation experi-ments, whereas the remaining ﬁve come from nitridationdata. The measured diffusivity ratios, each of which appearon the left hand side of one of the equations in the system aretabulated in Table II at the temperatures 1100 and 1000°C.A ratio greater than one implies a diffusivity enhancement,whereas smaller than one indicates retardation. In reality, thepoint defect concentrations during oxidation and nitridation,and therefore the diffusivity ratios are all functions of time.Although not explicit in the formulas, the quantities mea-sured at the end of the experiment are thus time and spaceaveraged values.We numerically solved the above mentioned system of ten equations using the following conservative bounds on thenonequilibrium point defect ratios:
FIG. 1. Diffusion proﬁles of 1000 °C, 5 h anneals under inert, oxidizing,and nitridizing ambients for
a
arsenic,
b
boron,
c
phosphorus,
d
an-timony,
e
30
silicon. The solid lines are the actual SIMS proﬁles measured,whereas the symbols show the simulation best ﬁts used for extracting dif-fusivity enhancements or retardations. The as-grown proﬁle for each case isalso given for reference.
6443J. Appl. Phys., Vol. 85, No. 9, 1 May 1999 Ural, Grifﬁn, and Plummer
Downloaded 06 Nov 2002 to 171.64.101.210. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp
C
I
ox
/
C
I
eq
1, 0
C
V
ox
/
C
V
eq
1, and
C
V
nit
/
C
V
eq
1, 0
C
I
nit
/
C
I
eq
1.
16
In doing so, we also allowed for
10% error in the measureddiffusivity ratios listed in Table II. The biggest contributor tothe error is the uncertainty in crater depth measurements of SIMS samples done by stylus proﬁlometry. This allowableerror value was chosen large enough so that a nonemptyrange existed satisfying all the criteria as summarized inTables III and IV. The bounds thereby obtained on the frac-tional contribution of each diffusion mechanism for eachdopant, along with the point defect perturbation levels, arelisted in the ﬁrst columns of Tables III and IV for the 1100and 1000°C anneals, respectively. For each unknown, thesmaller number is the minimum bound, whereas the largernumber is the maximum. These bounds indicate that B and Pdiffuse mostly by an interstitial mechanism, whereas Sb dif-fusion is mostly vacancy mediated. As and self-diffusion, onthe other hand, have both I and V components, and alsopossibly a contribution from the CE mechanism. The boundsobtained from the 1000°C experiment are closer togetherthan those from the 1100°C. This is a consequence of themathematical fact that higher levels of point defect injectionat the lower temperature aids in arriving at more restrictivevalues for the unknowns.More restrictive bounds can be obtained by making ap-proximations relating the perturbation levels of point defectsduring oxidation and nitridation. In the bulk, sufﬁcientlyaway from the surface, I and V recombine thermally to formsubstitutional silicon atoms and are generated from them viaEq.
8
. This process involves the creation and annihilationof I and V simultaneously, so their concentrations remaindependent. In addition, I and V can be singly created orannihilated at the surface independent of each other. There-fore, if the steady-state recombination and generation of Iand V in the bulk is dominant over surface generation andrecombination, we expect the relation of Eq.
13
to hold. Ingeneral, however, this relation is not satisﬁed. A detailedsolution of the relevant continuity equations,
19
as well asexperiments on short-time oxidation and nitridation
8
haveconcluded that, in general,1
C
V
ox
C
V
eq
C
I
eq
C
I
ox
and 1
C
I
nit
C
I
eq
C
V
eq
C
V
nit
.
17
The system of equations resulting from the data wassolved again using the constraints given by Eq.
17
insteadof the more relaxed ones represented by Eq.
16
. The resultsfor the fractional contributions are tabulated in the second
TABLE I. The extracted equilibrium
inert anneal
diffusion coefﬁcients forarsenic, boron, phosphorus, antimony, and
30
silicon at 1100 and 1000 °Cgiven in units of cm
2
/s.1100 °C 1000 °CArsenic 2.33
10
14
1.45
10
15
Boron 1.46
10
13
1.28
10
14
Phosphorus 1.38
10
13
1.32
10
14
Antimony 2.21
10
14
1.28
10
1530
Silicon 1.78
10
15
6.88
10
17
TABLE II. Diffusivity enhancements or retardations for arsenic, boron,phosphorus, antimony, and
30
silicon under nonequilibrium point defect con-ditions caused by oxidation and nitridation. Anneals were performed at1100 °C for 1 h and 1000 °C for 5 h.Oxidation Nitridation1100 °C 1000 °C 1100 °C 1000 °CArsenic 1.33 2.20 1.62 1.83Boron 3.07 4.70 0.421 0.341Phosphorus 2.51 3.84 0.356 0.350Antimony 0.391 0.266 3.18 3.78
30
Silicon 1.60 2.73 1.24 1.58TABLE III. Bounds on fractional contributions of I, V, and CE mechanisms of diffusion for As, B, P, Sb, and self-diffusion in Si obtained from 1100 °C 1h anneals. The ﬁrst column gives the solutions for the most general case, and the approximations made in the successive columns are noted in the headings.CE included CE included CE included No CE No CE No CE0
C
V
ox
/
C
V
eq
1
C
I
eq
C
I
ox
C
V
ox
C
V
eq
1
C
I
ox
C
V
ox
C
I
eq
C
V
eq
0
C
V
ox
/
C
V
eq
1
C
I
eq
C
I
ox
C
V
ox
C
V
eq
1
C
I
ox
C
V
ox
C
I
eq
C
V
eq
0
C
I
nit
/
C
I
eq
1
C
I
nit
C
V
nit
C
I
eq
C
V
eq
0
C
I
nit
/
C
I
eq
1
C
I
nit
C
V
nit
C
I
eq
C
V
eq
C
V
eq
C
V
nit
C
I
nit
C
I
eq
1
C
V
eq
C
V
nit
C
I
nit
C
I
eq
1
f
BI
0.84–1.00 0.94–1.00 0.94–0.99 0.86–1.00 0.98–1.00 0.98–0.99
f
PI
0.86–1.00 0.96–1.00 0.96–1.00 0.86–1.00 0.98–1.00 0.98–1.00
f
SbI
0–0.16 0–0.03 0–0.03 0–0.14 0–0.01 0–0.01
f
SiI
0.24–0.65 0.26–0.60 0.26–0.59 0.51–0.65 0.59–0.60 0.59
f
SiCE
0–0.62 0–0.62 0–0.62 0 0 0
f
SiV
0.09–0.49 0.10–0.41 0.11–0.41 0.35–0.49 0.40–0.41 0.41
f
AsI
0.15–0.54 0.17–0.47 0.17–0.47 0.36–0.54 0.42–0.47 0.42–0.47
f
AsCE
0–0.61 0–0.61 0–0.61 0 0 0
f
AsV
0.18–0.64 0.21–0.58 0.21–0.58 0.46–0.64 0.53–0.58 0.53–0.58
C
I
ox
/
C
I
eq
2.73–3.18 2.73–2.88 2.75–2.88 2.73–3.13 2.73–2.77 2.75–2.77
C
V
ox
/
C
V
eq
0–0.434 0.348–0.434 0.348–0.363 0–0.388 0.361–0.388 0.361–0.363
C
V
nit
/
C
V
eq
2.83–4.13 2.83–3.64 2.83–3.64 2.83–3.24 2.83–2.86 2.83–2.86
C
I
nit
/
C
I
eq
0–0.395 0.274–0.395 0.274–0.353 0–0.395 0.350–0.390 0.350–0.353
6444 J. Appl. Phys., Vol. 85, No. 9, 1 May 1999 Ural, Grifﬁn, and Plummer
Downloaded 06 Nov 2002 to 171.64.101.210. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

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